Capillaries are typically smaller than blood cells--about 5 μm in diameter. The pressure difference across the capillary is 0.7 kPa (measured for hamster skin) . If capillaries are ~1 mm long, how fast does the blood flow through, assuming it has the viscosity of water? How long therefore is a red cell in a typical capillary?

Explanation:

V = Flow rate

P = pressure difference = 0.7 x 10³ Pa

∩ = Viscosity = 8.9 x 10 ⁻⁴

L = length = 1 mm = 10⁻³ m

d = diameter = 5 x 10⁻⁶ m

r = radius = d/2 = 2.5 x 10⁻⁶ m

V = (π/8) (P r⁴) / (∩L)

V = (3.14 / 8) (0.7 x 10³ ) (2.5 x 10⁻⁶ )⁴ / (8.9 x 10⁻⁴ x 10⁻³ )

V = 1.21 x 10⁻¹⁴ m³/s

v = speed

A = Area of cross-section = π r² = 3.14 (2.5 x 10⁻⁶ )² = 1.9625 x 10⁻¹¹

Flow rate = V = Av

v = 1.21 x 10⁻¹⁴ / (1.9625 x 10⁻¹¹) = 0.000617 m/s

Time taken = length / v = 10⁻³ / 0.000617 = 1.621 sec

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